A-LevelMathematicsDifferentiation9709/33 · May/June 2017 · Q56 Marks
A curve has equation y = ¾ ln(1 + 3 cos²x) for 0 ≤ x ≤ ½π.
- (i)Express dy/dx in terms of tan x.[4]
- (ii)Hence find the x-coordinate of the point on the curve where the gradient is –1. Give your answer correct to 3 significant figures.[2]
Mark scheme
Marking points from the official mark scheme (May/June 2017). The mark or mark type is shown in brackets.
- [M1] Use the chain rule
- [A1] Obtain correct derivative in any form
- [M1] Use correct trigonometry to express derivative in terms of tan x
- [A1] Obtain dy/dx = -4 tan x / (4 + tan²x), or equivalent
- [M1] Equate derivative to –1 and solve a 3–term quadratic for tan x
- [A1] Obtain answer x=1.11 and no other in the given interval
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